Martha takes a road trip from point A to point B. She drives

Question

Martha takes a road trip from point A to point B. She drives x percent of the distance at 60 miles per hour and the remainder at 50 miles per hour. If Martha's average speed for the entire trip is represented as a fraction in its reduced form, in terms of x, which of the following is the numerator?

(A) 110
(B) 300
(C) 1,100
(D) 3,000
(E) 30,000

(A) 110
(B) 300
(C) 1,100
(D) 3,000
(E) 30,000

forrestgump · Accepted Answer

total distance = d

total time taken = x/(100*60) + (100-x)/(100*50)

speed = distance / time

gives numerator = 30000

HolaMaven · Answer

Assuming x=50, i.e. 50% road with speed of 60mph and remaining 50% with speed of 50mph.
Now knowing formula for average speed (when distance traveled is same) =  \frac{2ab}{a+b} , (a,b are speeds)
average speed in our case =  \frac{2*50*60}{50+60} = \frac{2*50*60}{110} = \frac{2*300}{11} 
Question asking in terms of x,i.e. 50% =  \frac{1}{2} 
thus  \frac{1}{2}*\frac{2*300}{11}*100 
Numerator = 30000
Thus  option E

christoph · Answer

total distance/total time=>d/((xd/100)/60+(d-(xd/100))/50)=>solve it and you will see that the numerator is 30000.

enigma123 · Answer

Martha takes a road trip from point A to point B. She drives x percent of the distance at 60 miles per hour and
the remainder at 50 miles per hour. If Martha's average speed for the entire trip is represented as a fraction
in its reduced form, in terms of x, which of the following is the numerator?

A)110
B) 300
C)1,100 
D)3,000 
E) 30,000

Guys - the answer for this question is not provided. I have calculated and got 30000 i.e. E. Can someone please tell me whether my answer is correct or incorrect?

kostyan5 · Answer

The correct answer is 300.

Let total distance = D.

d1 = xD/100 v1 = 60 t1 = d1/v1 = xD/6000
d2 = (1-x)D/100 v2 = 50 t2 = d2/v2 = (1-x)D/5000

For the total trip:

V = D/T = (d1+d2) / (t1+t2)

Note that (d1+d2) = D

V = \frac{D}{t1+t2}= \frac{D}{\frac{xD}{6000}+\frac{(1-x)D}{5000}}

For this it's easy to see that the numerator in reduced form will be the least common multiple of 5000 and 6000, which is 30,000.

Let me know if you need help on how to find the least common multiple.

EDIT: fixed expressing x in percent.

BDSunDevil · Answer

i keep getting 30,000.

@ kostyan5: x% 0f D is xD/100, so t1 is xD/6000 isn't it? 
what am i doing wrong?

kostyan5 · Answer

Yes, you are right. I didn't realize that percent (/100) doesn't cancel out at the end because there's on x in D. So we do need to express d1 and d2 in terms of x/100. I'm going to modify my solution above.

Sorry for the confusion. The answer is 30,000.

saikrishna123 · Answer

Question asks us for the fraction to be in its reduced form..

So if we solve, numerator will be 30 and not 30000....Where am I going wrong

gracie · Answer

let d=total distance
let x=fraction of distance driven at 60 mph
 d/ =300/(6-x) average speed
numerator=(300)(100)=30,000

shringi87 · Answer

an someone explain why this is being multiplies with 100 ??

Bunuel   VeritasPrepKarishma

ScottTargetTestPrep · Answer

Let d represent the distance between point A and point B.

d/

Multiplying by 30,000/30,000, we have:

30,000d/

Divide by d/d, we have:

30,000/

Answer: E

Kritisood · Answer

Let total distance be 100
Avg speed = total distance/ total time
Time 1 = x/60
Time 2 = (100-x)/50

Total time: x/60+(100-x)/50 = 600-x/300

Putting in formula: 30,000/600-x answer E

Kinshook · Answer

Given: Martha takes a road trip from point A to point B. She drives x percent of the distance at 60 miles per hour and the remainder at 50 miles per hour.

Asked: If Martha's average speed for the entire trip is represented as a fraction in its reduced form, in terms of x, which of the following is the numerator?

Let the distance between A & B be D miles

Total Distance = D miles
Total time taken = x%D/60 + (100%-x%)D/50 = xD/6000 + (100-x)D/5000 = {5xD + 6(100-x)D}/30000 = (600 - x)D/30000
Average Speed = 30000D/(600-x)D = 30000/(600-x)

IMO E

KarishmaB · Answer

"She drives  x percent  of the distance at 60 miles per hour" means that x is the 50 in case she drove 50% of the distance at 60 mph. x is not 0.5 in this case.
So, of a distance of 100, she drove x at 60 mph and (100 - x) at 50 mph.

Average Speed = \frac{100}{\frac{x}{60} + \frac{(100-x)}{50}} = \frac{30000}{600-x}

Answer (E)

djangobackend · Answer

why do you multiply by 100?

nishantswaft · Answer

Since there is a percent sign attached to the number.
When we remove the percent sign we multiply the number by 100.

Shubhradeep · Answer

to simplify, let distance be 100
x miles at 60 miles/hr and 100-x miles at 50 mile/hr

Total time taken =  \frac{x}{60} +  \frac{100-x}{50}  = T

In that case, average speed will be S =  \frac{100}{T}

Now simplifying T, we get T=  \frac{600-x}{300}

so S=  \frac{30000}{600-x}

Option E

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=87651 Harsha GMAT-Club-Forum-v4jmby0o.png

Martha takes a road trip from point A to point B. She drives

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